1. Cartesian coordinate system the geometric or graphical representation of a relation and/or function OR without geometry, algebra is pointless!

2. The first person to describe coordinates was Pierre de Fermat in a book of math investigations around 1629 but was not published until about 1679. But the system we know today bears its’ name from a man named Rene Descartes His modern version of (x,y) ordered pairs or coordinates known as the Cartesian coordinate system that uses axes to find the distance of a given point from an origin (0,0) was written about 1637.

3. The horizontal axis is also known as the x – axis and is used to plot the cause, input or independent quantity. The v e r t i c a l axis is also known as the y – axis and is used to plot the effect, output or dependent quantity. The modern coordinate system graphs the relation between two quantities as points or a set of points.

4. Remember ‘C’: Quadrant I Coordinates are (+,+) The origin (0,0) Quadrant II Coordinates are (-,+) Quadrant III Coordinates are (-,-) Quadrant IV Coordinates are (+,-)

5. Location of a point is given by an ordered pair with coordinates. Ex. (x, y) or (x, f(x)) The domain is all the x values that make sense for a particular relation. It can be continuous, in which every quantity between all the graphed x values makes sense. D: { 0 < x < ∞ } time (working) In this case time is continuous — all values between 0 and ? (however long you work) make sense.

6. The domain can also be discrete. It might have values between each point that do not make sense. Ex. D: {0, 1, 2, 3, 4} number of pets owned number of students Would all the values between each point make sense? Could a student own half a pet? The range is all the permissible y values. Ex. R: {1, 2, 6, 24}

7. Let’s consider the relation in the song you hear….. time (working hours) time (off hours) The maximum value (high point) for time off is 24 hours. The minimum (low point) hours off is 0. As x values of ‘time working’ increase, the y values of ‘time off’ decrease, so it is a decreasing function. The domain, or working hours, is continuous from 0 as all values from 0 make sense.

8. So time is love….. someone who waits for your time off may surprise you!

9. Cartesian coordinate system A. Murray 2012